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Ostrowski's Type Inequalities for (α, m)-Convex Function

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 3,  2010, pp.371-378
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.3.371
Title & Authors
Ostrowski's Type Inequalities for (α, m)-Convex Function
Ozdemir, Muhamet Emin; Kavurmaci, Havva; Set, Erhan;

Abstract
In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are ($\small{{\alpha}}$, m)-convex.
Keywords
($\small{{\alpha}}$, m)-Convex Function;m-Convex Function;Convex Function Ostrowski's Inequality;H$\small{\"{o}}$lder's Inequality;Power Mean Inequality;
Language
English
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References
1.
M. Alomari, M. Darus, S. S. Dragomir and P. Cerone, Ostrowski's inequalities for functions whose derivatives are s-convex in the second sense, RGMIA Res. Rep. Coll., 12(2009), Supplement, Article 15. [ONLINE: http://www.staff.vu.edu.au/RGMIA/v12(E).asp]

2.
M. K. Bakula, M. E. Ozdemir and J. Pecaric, Hadamard type inequalities for m-convex and (${\alpha},\;m$)-convex functions, J. Inequal. Pure & Appl. Math., 9(2008), Article 96, [ONLINE: http://jipam.vu.edu.au].

3.
M. Klaricic Bakula, J. Pecaric, and M. Ribicic, Companion inequalities to Jensen's inequality for m-convex and (${\alpha},\;m$)-convex functions, J. Inequal. Pure & Appl. Math., 7(2006), Article 194, [ONLINE: http://jipam.vu.edu.au].

4.
N. S. Barnett, P. Cerone, S. S. Dragomir, M. R. Pinheiro and A. Sofo, Ostrowski type inequalities for functions whose modulus of derivatives are convex and applications, RGMIA Res. Rep. Coll., 5(2)(2002), Article 1, [ONLINE: http://www.staff.vu.edu.au/RGMIA/v5n2.asp].

5.
S. S. Dragomir, Y. J. Cho and S. S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. of Math. Anal. Appl., 245(2)(2000), 489-501.

6.
S. S. Dragomir and A. Sofo, Ostrowski type inequalities for functions whose derivatives are convex, Proceedings of the 4th International Conference on Modelling and Simulation, November 11-13, 2002, Victoria University, Melbourne, Australia, RGMIA Res. Rep. Coll., 5(2002), Supplement, Article 30, [ONLINE: http://www.staff.vu.edu.au/RGMIA/v5(E).asp].

7.
V. G. Mihesan, A generalization of the convexity, Seminar on Functional Equations, Approx. and Convex., Cluj-Napoca (Romania) (1993).

8.
E. Set, M. E. Ozdemir and M.Z. Sarikaya, New inequalities of Ostrowski's type for s-convex functions in the second sense with applications, arXiv:1005.0702v1 [math.CA], May 5, 2010.

9.
G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1984, 329-338.